Equations And Inequations Ques 112
I. $2 x^{2}+15 x+27=0$
II. $2 y^{2}+7 y+6=0$
Directions : In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer
(1) if $x>y$
(2) if $x \geq y$
(3) if $x<y$
(4) if $x \leq y$
(5) if $x=y$ or the relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 112.(3)
Solution: (3) I. $2 x^{2}+15 x+27=0$
$\Rightarrow 2 x^{2}+6 x+9 x+27=0$
$\Rightarrow 2 x(x+3)+9(x+3)=0$
$\Rightarrow(x+3)(2 x+9)=0$
$\Rightarrow x=-3$ or, $\frac{-9}{2}$
II. $2 y^{2}+7 y+6=0$
$\Rightarrow 2 y^{2}+4 y+3 y+6=0$
$\Rightarrow 2 y(y+2)+3(y+2)=0$
$\Rightarrow(y+2)(2 y+3)=0$
$\Rightarrow y=-2$ or, $\frac{-3}{2}$
Clearly, $x<y$
BETA
